Mathematics

On the existence of Cournot-Nash equilibria in continuum games

Article Abstract:

A new feeble topology on the set of action profiles was introduced to obtain a substantial generalization of Cournot-Nash equilibrium existence in the usual continuum game model. The new feeble topology makes the action profiles much more general and eliminates the integrability of the action profiles. The generalization demonstrated that the existence of mixed equilibrium in the continuum model not only indicates the existence of pure equilibrium, but that mixed equilibrium follows from pure equilibrium.

Singularity theory and core existence in the spatial model

Article Abstract:

The conclusions derived by Schofield and McKelvey from their study of a spatial model using the singularity theory are supported by erroneous proofs. At issue is the case of a voting game whose outcome space is significantly of large dimension and which consequently results in the absence of a core outcome for practically every utility profile. An alternative approach to determining the correct bounds for the model is presented.